/export/starexec/sandbox/solver/bin/starexec_run_c_complexity /export/starexec/sandbox/benchmark/theBenchmark.c /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?, O(n^1)) proof of /export/starexec/sandbox/output/output_files/bench.koat # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The runtime complexity of the given CpxIntTrs could be proven to be BOUNDS(1, n^1). (0) CpxIntTrs (1) Koat Proof [FINISHED, 378 ms] (2) BOUNDS(1, n^1) ---------------------------------------- (0) Obligation: Complexity Int TRS consisting of the following rules: eval_foo_start(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb0_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: TRUE eval_foo_bb0_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_x, v_y, v_3, v_4, v_x, v_y)) :|: TRUE eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb2_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: v_.0 >= 0 && v_.01 >= 1 eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: v_.0 < 0 eval_foo_bb1_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb3_in(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: v_.01 < 1 eval_foo_bb2_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_1(v_.0, v_.01, v_.0 - v_.01, v_4, v_x, v_y)) :|: TRUE eval_foo_1(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_2(eval___VERIFIER_nondet_int_start(v_.0, v_.01, v_3, v_4, v_x, v_y), eval_foo_2(v_.0, v_.01, v_3, nondef.0, v_x, v_y)) :|: TRUE eval_foo_2(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_bb1_in(v_3, v_4, v_3, v_4, v_x, v_y)) :|: TRUE eval_foo_bb3_in(v_.0, v_.01, v_3, v_4, v_x, v_y) -> Com_1(eval_foo_stop(v_.0, v_.01, v_3, v_4, v_x, v_y)) :|: TRUE The start-symbols are:[eval_foo_start_6] ---------------------------------------- (1) Koat Proof (FINISHED) YES(?, 36*Ar_1 + 44) Initial complexity problem: 1: T: (Comp: ?, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 0 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - Ar_2, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_6, Ar_6)) (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Repeatedly propagating knowledge in problem 1 produces the following problem: 2: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 0 /\ Ar_2 >= 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - Ar_2, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_6, Ar_6)) (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 A polynomial rank function with Pol(evalfoostart) = 2 Pol(evalfoobb0in) = 2 Pol(evalfoobb1in) = 2 Pol(evalfoobb2in) = 2 Pol(evalfoobb3in) = 1 Pol(evalfoo1) = 2 Pol(evalfoo10) = 0 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoo11) = 2 Pol(evalfoo2) = 2 Pol(evalfoostop) = 0 Pol(koat_start) = 2 orients all transitions weakly and the transitions evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 + 1 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_2 ] strictly and produces the following problem: 3: T: (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_0 >= 0 /\ Ar_2 >= 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_0 + 1 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 >= Ar_2 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - Ar_2, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: ?, Cost: 1) evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_6, Ar_6)) (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] start location: koat_start leaf cost: 0 Applied AI with 'oct' on problem 3 to obtain the following invariants: For symbol evalfoo1: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfoo10: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfoo11: X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfoo2: X_6 - X_7 >= 0 /\ -X_6 + X_7 >= 0 /\ X_2 - X_5 - 1 >= 0 /\ X_1 - X_5 - 1 >= 0 /\ X_3 + X_5 >= 0 /\ X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfoobb1in: -X_1 + X_2 >= 0 For symbol evalfoobb2in: X_3 - 1 >= 0 /\ X_2 + X_3 - 1 >= 0 /\ X_1 + X_3 - 1 >= 0 /\ X_2 >= 0 /\ X_1 + X_2 >= 0 /\ -X_1 + X_2 >= 0 /\ X_1 >= 0 For symbol evalfoobb3in: -X_1 + X_2 >= 0 This yielded the following problem: 4: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 ] (Comp: ?, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 - Ar_6 >= 0 /\ -Ar_5 + Ar_6 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_6, Ar_6)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: ?, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - Ar_2, Ar_5, Ar_6)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: ?, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) start location: koat_start leaf cost: 0 A polynomial rank function with Pol(koat_start) = 6*V_2 + 6 Pol(evalfoostart) = 6*V_2 + 6 Pol(evalfoobb3in) = 6*V_1 Pol(evalfoostop) = 6*V_1 Pol(evalfoo2) = 6*V_3 + 6*V_5 + 1 Pol(evalfoobb1in) = 6*V_1 + 6 Pol(evalfoo1) = 6*V_3 + 6*V_5 + 4 Pol(evalfoo10) = 1 Pol(evalfoo11) = 6*V_3 + 6*V_5 + 2 Pol(evalVERIFIERnondetintstart) = 0 Pol(evalfoobb2in) = 6*V_1 + 5 Pol(evalfoobb0in) = 6*V_2 + 6 orients all transitions weakly and the transitions evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - Ar_2, Ar_5, Ar_6)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ] evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 - Ar_6 >= 0 /\ -Ar_5 + Ar_6 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_6, Ar_6)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] strictly and produces the following problem: 5: T: (Comp: 1, Cost: 0) koat_start(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ 0 <= 0 ] (Comp: 2, Cost: 1) evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoostop(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 ] (Comp: 6*Ar_1 + 6, Cost: 1) evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_4, Ar_1, Ar_5, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_5 - Ar_6 >= 0 /\ -Ar_5 + Ar_6 >= 0 /\ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 6*Ar_1 + 6, Cost: 1) evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_2(evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0), evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Fresh_0)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 6*Ar_1 + 6, Cost: 1) evalfoo11(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo2(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_6, Ar_6)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 6*Ar_1 + 6, Cost: 1) evalfoo10(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalVERIFIERnondetintstart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ Ar_1 - Ar_4 - 1 >= 0 /\ Ar_0 - Ar_4 - 1 >= 0 /\ Ar_2 + Ar_4 >= 0 /\ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 6*Ar_1 + 6, Cost: 1) evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoo1(Ar_0, Ar_1, Ar_2, Ar_3, Ar_0 - Ar_2, Ar_5, Ar_6)) [ Ar_2 - 1 >= 0 /\ Ar_1 + Ar_2 - 1 >= 0 /\ Ar_0 + Ar_2 - 1 >= 0 /\ Ar_1 >= 0 /\ Ar_0 + Ar_1 >= 0 /\ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_2 ] (Comp: 2, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb3in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ 0 >= Ar_0 + 1 ] (Comp: 6*Ar_1 + 6, Cost: 1) evalfoobb1in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb2in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) [ -Ar_0 + Ar_1 >= 0 /\ Ar_0 >= 0 /\ Ar_2 >= 1 ] (Comp: 1, Cost: 1) evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb1in(Ar_1, Ar_1, Ar_3, Ar_3, Ar_4, Ar_5, Ar_6)) (Comp: 1, Cost: 1) evalfoostart(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6) -> Com_1(evalfoobb0in(Ar_0, Ar_1, Ar_2, Ar_3, Ar_4, Ar_5, Ar_6)) start location: koat_start leaf cost: 0 Complexity upper bound 36*Ar_1 + 44 Time: 0.340 sec (SMT: 0.258 sec) ---------------------------------------- (2) BOUNDS(1, n^1)